Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x-y &= -2 \\ -5x+y &= -2\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-5x = -y-2$ Divide both sides by $-5$ to isolate $x$ $x = {\dfrac{1}{5}y + \dfrac{2}{5}}$ Substitute this expression for $x$ in the first equation. $7({\dfrac{1}{5}y + \dfrac{2}{5}}) - y = -2$ $\dfrac{7}{5}y + \dfrac{14}{5} - y = -2$ Simplify by combining terms, then solve for $y$ $\dfrac{2}{5}y + \dfrac{14}{5} = -2$ $\dfrac{2}{5}y = -\dfrac{24}{5}$ $y = -12$ Substitute $-12$ for $y$ in the top equation. $7x+ 12 = -2$ $7x+12 = -2$ $7x = -14$ $x = -2$ The solution is $\enspace x = -2, \enspace y = -12$.